Research Interests of Sean Sather-Wagstaff
RESEARCH TOPICS
commutative algebra
homological algebra
(co)homology (including relative and Tate (co)homology)
(semi)dualizing modules and complexes
ascent of module structures
Bass numbers and Betti numbers
homological dimensions
divisor class groups
RESEARCH SUMMARIES
CV
(Last updated 10 Feb 2014)
Research Statement
(Last updated 05 Nov 2013)
REFEREED LECTURE NOTES
A somewhat gentle introduction to differential graded commutative algebra
, with Kristen A. Beck, 78 pages, Connections between Algebra and Geometry (Springer) to appear.
REFEREED RESEARCH PAPERS
Multiplicities and a dimension inequality for unmixed modules
, Journal of Algebra
238
(2001), 372-388.
arXiv version
A dimension inequality for Cohen-Macaulay rings
, Transactions of the American Mathematical Society
354
(2002), 993-1005.
Intersections of symbolic powers of prime ideals
, Journal of the London Mathematical Society (2)
65
(2002), no. 3, 560--574.
arXiv version
On symbolic powers of prime ideals
, Commutative algebra. Interactions with Algebraic Geometry, Contemporary Math.
331
(2003), 329-342.
G-dimension over local homomorphisms. Applications to the Frobenius endomorphism
, with
Srikanth Iyengar
, Illinois Journal of Mathematics
48
(2004), no. 1, 241--272.
arXiv version
Complete intersection dimensions for complexes
, Journal of Pure and Applied Algebra
190
(2004), no. 3, 267--290.
arXiv version
Characterizing local rings via homological dimensions and regular sequences
, with
Shokrollah Salarian
and
Siamak Yassemi
, Journal of Pure and Applied Algebra
207
(2006), no. 1, 99--108.
arXiv version
The set of semidualizing complexes is a nontrivial metric space
, with
Anders Frankild
, Journal of Algebra
308
(2007), no. 1, 124-143.
arXiv version
Reflexivity and ring homomorphisms of finite flat dimension
, with
Anders Frankild
. Communications in Algebra
35
(2007), no. 2, 461--500.
arXiv version
Semidualizing modules and the divisor class group
, Illinois Journal of Mathematics
51
(2007), no. 1, 255-285.
arXiv version
Detecting completeness from Ext-vanishing
, with
Anders J. Frankild
, Proceedings of the American Mathematical Society
136
(2008), no. 7, 2303-2312.
arXiv version
.
Stability of Gorenstein categories
, with
Tirdad Sharif
and
Diana White
, Journal of the London Mathematical Society (2)
77
(2008), no. 2, 481-502.
arXiv version
.
An Euler characteristic for modules of finite G-dimension
, with
Diana White
, Mathematica Scandinavica
102
(2008), no. 2, 206-230.
Ascent of module structures, vanishing of Ext, and extended modules
, with
Anders J. Frankild
and
Roger A. Wiegand
, Michigan Mathematical Journal,
57
(2008), 321--337.
arXiv version
Complete intersection dimensions and Foxby classes
, Journal of Pure and Applied Algebra
212
(2008), no. 12, 2594-2611.
arXiv version
A Cohen-Macaulay algebra has only finitely many semidualizing modules
, with
Lars Winther Christensen
, Mathematical Proceedings of the Cambridge Philosophical Society
145
(2008), no. 3, 601-603.
arXiv version
Gorenstein cohomology in abelian categories
, with
Tirdad Sharif
and
Diana White
, Journal of Mathematics of Kyoto University,
48
(2008), no. 3, 571-596.
Relations between semidualizing complexes
, with
Anders J. Frankild
and
Amelia Taylor
, Journal of Commutative Algebra,
1
(2009), no. 3, 393-436.
arXiv version
Maps on Divisor Class Groups Induced by Ring Homomorphisms of Finite Flat Dimension
, with
Sandra Spiroff
, Journal of Commutative Algebra,
1
(2009), no. 3, 567-590.
arXiv Version
Modules of finite homological dimension with respect to a semidualizing module
, with
Siamak Yassemi
, Archiv der Mathematik (Basel),
93
(2009), no. 2, 111-121.
arXiv version
Descent via Koszul extensions
, with
Lars Winther Christensen
, Journal of Algebra,
322
(2009), no. 9, 3026-3046.
arXiv version
Bass Numbers and Semidualizing Complexes
, Commutative Algebra and its Applications, de Gruyter, (2009), 349-381.
arXiv version
Transfer of Gorenstein dimensions along ring homomorphisms
, with
Lars Winther Christensen
, Journal of Pure and Applied Algebra,
214
, (2010), no. 6, 982-989.
arXiv version
Comparison of relative cohomology theories with respect to semidualizing modules
, with
Tirdad Sharif
and
Diana White
, Mathematische Zeitschrift,
264
, (2010), no. 3, 571-600.
arXiv version
Tate cohomology with respect to semidualizing modules
, with
Tirdad Sharif
and
Diana White
, Journal of Algebra,
324
, (2010), no. 9, 2336-2368.
arXiv version
Rings that are homologically of minimal multiplicity
, with
Keivan Borna
and
Siamak Yassemi
, Communications in Algebra,
39
, (2011), no. 3, 782-807.
arXiv version
AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules
, with
Tirdad Sharif
and
Diana White
, Algebras and Representation Theory,
14
, (2011), no. 3, 403-428.
arXiv version
Homology of artinian and Matlis reflexive modules, I
, with
Bethany Kubik
and Micah J. Leamer, Journal of Pure and Applied Algebra,
215
, (2011), no. 10, 2486--2503.
arXiv version
Second symmetric powers of chain complexes
, with
Anders J. Frankild
and
Amelia Taylor
, Bulletin of the Iranian Mathematical Society,
37
(2011), no. 3, 39-75.
arXiv version
Lower bounds for the number of semidualizing complexes over a local ring
, Mathematica Scandinavica
110
(2012), no. 1, 5-17.
arXiv version
Presentations of rings with non-trivial semidualizing modules
, with
David A. Jorgensen
and
Graham J. Leuschke
, Collectanea Mathematica
63
(2012), no. 2, 165-180.
arXiv version
Regular Pullbacks
, with
Jason Boynton
, Progress in Commutative Algebra 2, de Gruyter (2012), 145-169.
On Zero Divisor Graphs
, with
Jim Coykendall
,
Laura Sheppardson
, and
Sandra Spiroff
, Progress in Commutative Algebra 2, de Gruyter (2012), 241-299.
Liftings and Quasi-Liftings of DG modules
, with
Saeed Nasseh
, Journal of Algebra,
373
(2013), 162-182.
arXiv version
Embedding modules of finite homological dimension
, Glasgow Mathematical Journal,
55
(2013), no. 1, 85-96.
arXiv version
Edge ideals of weighted graphs
, with Chelsey Paulsen, Journal of Algebra and its Applications,
12
(2013), no. 5, p-q.
arXiv version
Krull Dimension for Differential Graded Algebras
, with
Kristen A. Beck
, Archiv der Mathematik (Basel),
101
, (2013), no. 2, 111-119.
arXiv version
Decompositions of Monomial Ideals in Real Semigroup Rings
, with Daniel Ingebretson, Communications in Algebra,
41
, (2013), no. 11, 4363-4377.
arXiv version
Multiplicities of semidualizing modules
, with
Susan M. Cooper
, Communications in Algebra,
41
, (2013), no. 12, 4549-4558.
arXiv version
Homology of artinian and Matlis reflexive modules, II
, with
Bethany Kubik
and Micah J. Leamer, Journal of Algebra,
403
, (2014), no. 1, 229-272.
arXiv version
Relative Tor functors with respect to a semidualizing module
, with
Maryam Salimi
,
Elham Tavasoli
, and
Siamak Yassemi
, 15 pages, Algebras and Representation Theory,
17
, no. 1 (2014), 103-120. (The
arXiv version
is 29 pages long and contains more details.)
NAK for Ext and Ascent of module structures
, with
Benjamin J. Anderson
, 9 pages. Proceedings of the American Mathematical Society,
142
(2014), 1165-1174.
arXiv version
Cohen factorizations: weak functoriality and applications
, with
Saeed Nasseh
, 24 pages, Journal of Pure and Applied Algebra, to appear.
Reflexivity and connectedness
, 10 pages, Glasgow Mathematical Journal, to appear.
A local ring has only finitely many semidualizing complexes up to shift-isomorphism
, with
Saeed Nasseh
, 31 pages, submitted.
Contracting endomorphisms and dualizing complexes
, with
Saeed Nasseh
, 25 pages, submitted.
Ascent properties for derived functors
, 6 pages, submitted.
Torsion in kernels of induced maps on divisor class groups
, with
Sandra Spiroff
, 19 pages, submitted.
Krull dimension of monomial ideals in polynomial rings with real exponents
, with Zechariah Andersen, 22 pages, submitted.
Relative Homology and Gorenstein Flat Dimension
, with Tirdad Sharif and Diana White, 19 pages, submitted.
Local rings of embedding codepth at most 3 have only trivial semidualizing complexes
, with
Saeed Nasseh
, 9 pages, submitted.
On the structure of $S_2$-ifications of complete local rings
, with
Sandra Spiroff
, 14 pages, submitted.
Support and cofiniteness for complexes
, with Richard Wicklein, 20 pages, submitted.
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Last updated 27 Mar 2014.